solar physics & space plasma research centre

Solar Physics & Space Plasma Research Centre

University of Sheffield

Ionization diagnostics of solar magnetic structures

Dr Gary [email protected]

Can observed waves tell us anything at all about spicules?



Acknowledgements

Prof. Marcel Goossens, Dr. Roberto Soler , Dr. Jesse Andries

Dr. Jaume Terradas

Dr. Jiansen He

Prof. Robertus Erdélyi, Prof. Michael Ruderman



Plasma density measurements from intensity

Traditionally using spectral line intensities. Assuming filling factor, background subtraction, etc. correct still forced to make many assumptions.

Intensity

Source function

Opacity

Plasma density

Geometric depth



Spicule filling factor?

Spicules very narrow features at spatial resolution limit of telescopes, e.g., SOT (approx. 200 km).

Unresolved expanding flux tube

De Forest (2007)



Spicule plasma density modelling

Density model from eclipse flash spectra (Makita 2003).

Assumptions

1) constant source function

2) intensity of metallic lines ∝ intensity of hydrogen density (Zirker 1958)

3) Balmer line intensity ∝ ne np

(isothermal plasma assumption)

4) Height dependent spicule filling factor 0.01-1.01



Spicule magnetic field measurementFrom Centeno et al. (2010). S/N ratio poor for off-limb Zeeman and Hanle measurements. Integration time of 45 minutes at two different altitudes (2’’ and 3” above limb). Much longer than lifetime of individual spicules.



Example of propagating kink wave observed in spicule with Hinode/SOT Ca II H filter from He et al. (2009). Relatively undynamic “Type I” spicule.

Can we use wave observations to say something about spicule structure?

Flow speed (up and down) ≈ 10 km s-1

Phase speed ≈100 km s-1

→ Sub-Alfvenic flow (not always the case!)


University of SheffieldTime (0 - 360s)

Heig

ht (0

- 7

Mm

)

Can measure the follow crucial wave parameters as a function of height (He et al. 2009)

1) Period

2) Phase travel time (→phase speed)

3) Velocity amplitude

Wave propagates along the spicule in about 150 s, well within the spicule lifetime.

Amplitude vs height and time



Wave properties vs height

From He et al. (2009). See also earlier work by Zaqarashvili et al. (2007)

Using ideal MHD

Allow internal and external plasma density to be different

Assume average R dependence for magnetic field, i.e,



Basic model



Governing wave equations m=0 (the “torsional Alfven wave”) m=1 (the “kink wave”)

See e.g. Hollweg (1981), Poedts et al. (1985).

Verth & Erdélyi (2008), Ruderman et al. (2008), Andries & Cally (2011)

N.B. not the same as equation by Spruit (1981)!



Basic kink wave behaviour (no damping)

WKB solution for velocity amplitude is

1)

2)

3)



Observational examples

In study by He et al. (2009) they use Hinode/SOT to measure amplitudes and wavelengths in spicules. Are there understandable trends here?



Effect of dampingFollowing on from Roberto’s talk. Ion-neutral damping is a frequency dependent effect.

To compete with damping due to resonant absorption need

Martinez-Sykora et al. (2012) Okamoto & De Pontieu (2011).



Effect of resonant absorption

In the TTTB approximation damping length due to RA was investigated by Terradas et al. (2010), Verth et al. (2010) and Soler et al. (2011)

Equilibrium type Damping relation



Effect of RA: example 1

Assume a straight tube (constant magnetic field ), constant density



Effect of RA:example 2

Assume a expanding tube (non-constant magnetic field) and non-constant density so that kink speed varies.



Velocity amplitude: Coronal holesThe trend in non-thermal spectral line broadening (interpreted as velocity amplitude) has been claimed to be the source for both coronal heating and solar wind acceleration (Hahn et al. 2012, Bemporad & Abbo 2012)

McIntosh et al. (2011) used SDO/AIA to estimate phase speed with height.

Measured average velocity amplitude of 25 km s-1

It is well known (Kneser`s oscillation theorem) that the governing kink wave equation can have a cutoff if is increasing linearly with height (or greater).



Cutoff frequency

Linear profile Quadratic profile



Spicule statistics Okamoto & De Pontieu (2011) studied wave properties of large sample.

59% propagating up 21% propagating down20% standing

1) High pass filtering due to longitudinal stratification (cutoff frequency)

2) Low pass filtering caused by transverse stratification (resonant absorption or ion-neutral damping)



Case study: Verth et al. (2011)

From observational case study of He at al. (2009) , all wave variables, apart from R(s), can be estimated.

where



Least squares fit to data: Phase travel time



Least squares fit to data: Velocity amplitude



Spicule flux tube area vs height

Tsuneta et al. (2008) estimated upper limit area expansion of 345 between photosphere and corona (in Sun’s south polar region).

Tu et al. (2005)



Spicule magnetic field strength vs heightComparison with average unsigned magnetic field from 3D radiative MHD simulations of De Pontieu et al. (2007) (courtesy M. Carlsson).



Comparison of footpoint magnetic field

Comparison between wave study result and 3D radiative MHD simulation highly dubious! A dipole structure at footpoint of spicule, c.f., simulation?



Spicule plasma density vs height

Electron densitySpectroscopic studies of Becker (1968), Makita (2003)

Plasma densitySpectroscopic study of Makita (2003)

Estimate using kink wave observation by Verth et al. (2011)

TEMPERATURE INCREASE WITH HEIGHT (De Pontieu et al. 2011)?



Assuming plasma density is proportional to hydrogen number density and most free electrons are from hydrogen then ionisation fraction is

Makita (2003) estimate plotted for comparison.

Spicule ionisation fraction vs heightBy combining wave observation (plasma density scale gradient) and spectroscopy (electron density gradient) can estimate ionisation fraction.



Conclusions

Studying waves can give insight into the height dependence of both magnetic field and plasma mass density. Not

without value in the chromosphere!

Need good estimates of both height dependence of phase speed and velocity amplitude. One without the other not very useful. Although can say something about cutoff frequency with just phase speed.

Can studying waves tell us anything about ionisation? Certainly can help with estimating height dependence of mass density in chromosphere. Not without value!

Damping regime due to ion-neutral collisions interesting. High frequency effect. Would be difficult to disentangle from other damping effects, e.g. resonant absorption (also frequency dependent).

solar physics & space plasma research centre

Documents

external plasma density

velocity amplitude wave

wave observations

spicule lifetime

propagating kink wave

spicule structure

amplitude vs height

torsional alfven wave